A B-spline surface interpolator for precision machining of free-form surfaces

This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization of tensor product splines, are adopted. The basic idea of this paper is to fit large scale data with a tensorial B-spline surface and to refine the surface until a specified tolerance is met. Since some isolated domains exceeding tolerance may result, detail features on these domains are modeled by a tensorial B-spline basis with a finer resolution, superimposed by employing the PB-spline approach. The present method leads to an efficient model of free form surfaces, since both large scale data and local geometrical details can be efficiently fitted. Two application examples are presented. The first one concerns the fitting of a set of data points sampled from an interior car trim with a central geometrical detail. The second one refers to the modification of the tensorial B-spline surface representation of a mould in order to create a local adjustment. Considerations regarding strengths and limits of the approach then follow.

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Automatic Polishing of Super Accuracy Mirror Mold with Free-Form Surface by Curvature Analysis

Materials Science Forum ◽

10.4028/www.scientific.net/msf.505-507.547 ◽

2006 ◽

Vol 505-507 ◽

pp. 547-552 ◽

Cited By ~ 2

Author(s):

Ming June Tsai ◽

Jing Jing Fang ◽

Jian Feng Huang

Keyword(s):

Free Form ◽

Mold Surface ◽

B Spline ◽

Curvature Analysis ◽

Spline Surface ◽

Effective Contact ◽

Automatic Polishing ◽

Contact Width ◽

Free Form Surface ◽

Free Form Surfaces

This paper proposed a polishing path planning method of super accuracy mirror mold with free-form surface by curvature analysis. First, IGES files of free-form surfaces are read and the mold geometry is regenerated as B-spline surface by the Automatic Mold Polishing System (AMPS). By using the derivative properties of B-spline surface, normal vector and principal curvatures at any point of the surface are calculated. In addition, the effective contact width between polishing tool and mold surface based on the grain size and the principal radii of curvature is also determined. The minimum contact width in 3-D is mapped onto the (u, v) parameters of B-spline surface. Then a modified Peano fractal path with weaving function is calculated based on the effective contact width in the (u, v) coordinate. This Peano-weaving path was tested on an optical mold with free-form surface. The polishing result shows the method is very effective and achieves the level of mirror surface with roughness Ra 29nm.

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Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme

Journal of Science and Technology Issue on Information and Communications Technology ◽

10.31130/jst.2017.41 ◽

2017 ◽

Vol 3 (1) ◽

pp. 82

Author(s):

Nga Le-Thi-Thu ◽

Khoi Nguyen-Tan ◽

Thuy Nguyen-Thanh

Keyword(s):

Free Form ◽

Subdivision Scheme ◽

B Spline ◽

Geometric Fitting ◽

Arbitrary Topology ◽

Spline Surface ◽

Spline Surfaces ◽

Low Degree ◽

Data Points ◽

Free Form Surfaces

Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adjusted locally by a simple geometric fitting algorithm to increase the accuracy of the obtained B-spline. The reconstructed B-spline having the low degree along with arbitrary topology is interpolative to most of the given data points after some fitting steps without solving any linear system. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Results show that this approach is simple, fast, flexible and can be successfully applied to a variety of surface shapes.

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Tool Path Generation for Free-Form Surfaces Using B-Spline Surface

Lecture Notes in Mechanical Engineering - Proceedings of the International Conference on Research and Innovations in Mechanical Engineering ◽

10.1007/978-81-322-1859-3_6 ◽

2014 ◽

pp. 57-71

Author(s):

Simranpreet Singh Randhawa ◽

Jaswinder Singh Saini

Keyword(s):

Tool Path ◽

Tool Path Generation ◽

Free Form ◽

Path Generation ◽

B Spline ◽

Spline Surface ◽

Free Form Surfaces

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Computation of Voxel Maps Containing Tool Access Directions for Machining Free-Form Shapes

Volume 1: Design for Manufacturing Conference ◽

10.1115/96-detc/dfm-1408 ◽

1996 ◽

Author(s):

Johan W. H. Tangelder ◽

Joris S. M. Vergeest ◽

Mark H. Overmars

Keyword(s):

Free Form ◽

Geometric Accuracy ◽

Surface Sampling ◽

B Spline ◽

Spline Surface ◽

Surface Data

Abstract An algorithm that derives tool access directions for machining free-form shapes is presented. A free-form shape to be machined is given by a preliminary B-spline model. We allow that the B-spline surface data are as inaccurate as the user-selected geometric accuracy of the prototype to be machined. Using surface sampling a visibility voxel map is obtained. From this map a voxel map is derived that contains per voxel a set of tool access directions. From the obtained voxel map regions can be selected that can be machined with a fixed tool access direction per region.

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Measurement point sampling method for inspection of parts with free-form surfaces

Advances in Mechanical Engineering ◽

10.1177/1687814018809577 ◽

2018 ◽

Vol 10 (11) ◽

pp. 168781401880957 ◽

Cited By ~ 4

Author(s):

Dezhong Zhao ◽

Wenhu Wang ◽

Jinhua Zhou ◽

Ruisong Jiang ◽

Kang Cui ◽

...

Keyword(s):

Measurement Accuracy ◽

Sampling Method ◽

Free Form ◽

Surface Inspection ◽

B Spline ◽

Spline Curves ◽

Data Points ◽

Manufacturing Accuracy ◽

Method Of Measurement ◽

Free Form Surfaces

Parts must be measured to evaluate the manufacturing accuracy in order to check whether their dimension is in expected tolerance. In engineering, parts with free-form surfaces are generally measured by high-precision coordinate-measuring machines. The measurement accuracy is usually improved by increasing the density of measurement points, which is time-consuming and costly. In this article, a novel sampling method of measurement points for free-form surface inspection is proposed. First, surface inspection is simplified into the inspection of a number of section curves of the surface. Second, B-spline curves constructed with an iterative method are employed to approximate these section curves. Subsequently, data points necessary to construct the B-spline curves are taken as the measurement points. Finally, the proposed method is compared with other two sampling methods. The results indicate that the proposed method greatly reduced the number of measurement points without decreasing the precision of surface modeling.

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A Generic Approach to Free Form Surface Generation

Journal of Computing and Information Science in Engineering ◽

10.1115/1.1559579 ◽

2002 ◽

Vol 2 (4) ◽

pp. 294-301 ◽

Cited By ~ 2

Author(s):

J. Cotrina-Navau ◽

N. Pla-Garcia ◽

M. Vigo-Anglada

Keyword(s):

Theoretical Approach ◽

Differentiable Manifold ◽

Surface Generation ◽

Free Form ◽

B Spline ◽

Free Form Surface ◽

Manifold Theory ◽

Free Form Surfaces

A theoretical approach to construct free form surfaces is presented. We develop the concepts that arise when a free form surface is generated by tracing a mesh, using differentiable manifold theory, and generalizing the B-spline scheme. This approach allows us to define a family of practical schemes. Four different applications of the generic approach are also presented in this paper.

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